Trigonometry, (8th Edition) (Available 2011 Titles Enhanced Web Assign)

627 Pages·2010·29.53 MB·English

by  Ron Larson

Trigonometry
Eighth Edition
Ron Larson
The Pennsylvania State University
The Behrend College
With the assistance of
David C. Falvo
The Pennsylvania State University
The Behrend College
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Trigonometry, Eighth Edition © 2011, 2007 Brooks/Cole, Cengage Learning
Ron Larson
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Contents
A Word from the Author (Preface) vi
chapter P Prerequisites 1
P.1 Review of Real Numbers and Their Properties 2
P.2 Solving Equations 15
P.3 The Cartesian Plane and Graphs of Equations 29
P.4 Linear Equations in Two Variables 43
P.5 Functions 58
P.6 Analyzing Graphs of Functions 73
P.7 A Library of Parent Functions 85
P.8 Transformations of Functions 92
P.9 Combinations of Functions: Composite Functions 102
P.10 Inverse Functions 111
Chapter Summary 121 Review Exercises 124
Chapter Test 129 Proofs in Mathematics 130
Problem Solving 131
chapter 1 Trigonometry 133
1.1 Radian and Degree Measure 134
1.2 Trigonometric Functions: The Unit Circle 146
1.3 Right Triangle Trigonometry 153
1.4 Trigonometric Functions of Any Angle 164
1.5 Graphs of Sine and Cosine Functions 173
1.6 Graphs of Other Trigonometric Functions 184
1.7 Inverse Trigonometric Functions 195
1.8 Applications and Models 205
Chapter Summary 216 Review Exercises 218
Chapter Test 221 Proofs in Mathematics 222
Problem Solving 223
chapter 2 Analytic Trigonometry 225
2.1 Using Fundamental Identities 226
2.2 Verifying Trigonometric Identities 234
2.3 Solving Trigonometric Equations 241
2.4 Sum and Difference Formulas 252
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iv Contents
2.5 Multiple-Angle and Product-to-Sum Formulas 259
Chapter Summary 270 Review Exercises 272
Chapter Test 275 Proofs in Mathematics 276
Problem Solving 279
chapter 3 Additional Topics in Trigonometry 281
3.1 Law of Sines 282
3.2 Law of Cosines 291
3.3 Vectors in the Plane 299
3.4 Vectors and Dot Products 312
Chapter Summary 322 Review Exercises 324
Chapter Test 328 Cumulative Test for Chapters 1–3 329
Proofs in Mathematics 331 Problem Solving 335
chapter 4 Complex Numbers 337
4.1 Complex Numbers 338
4.2 Complex Solutions of Equations 345
4.3 Trigonometric Form of a Complex Number 353
4.4 DeMoivre's Theorem 360
Chapter Summary 366 Review Exercises 368
Chapter Test 371 Proofs in Mathematics 372
Problem Solving 373
chapter 5 Exponential and Logarithmic Functions 375
5.1 Exponential Functions and Their Graphs 376
5.2 Logarithmic Functions and Their Graphs 387
5.3 Properties of Logarithms 397
5.4 Exponential and Logarithmic Equations 404
5.5 Exponential and Logarithmic Models 415
Chapter Summary 428 Review Exercises 430
Chapter Test 433 Proofs in Mathematics 434
Problem Solving 435
Contents v
chapter 6 Topics in Analytic Geometry 437
6.1 Lines 438
6.2 Introduction to Conics: Parabolas 445
6.3 Ellipses 454
6.4 Hyperbolas 463
6.5 Rotation of Conics 473
6.6 Parametric Equations 481
6.7 Polar Coordinates 489
6.8 Graphs of Polar Equations 495
6.9 Polar Equations of Conics 503
Chapter Summary 510 Review Exercises 512
Chapter Test 515 Cumulative Test for Chapters 4–6 516
Proofs in Mathematics 518 Problem Solving 521
Answers to Odd-Numbered Exercises and Tests A1
Index A81
Index of Applications (web)
Appendix A Concepts in Statistics (web)
A.1 Representing Data
A.2 Measures of Central Tendency and Dispersion
A.3 Least Squares Regression
A Word from
the Author
Welcome to the Eighth Edition of Trigonometry! We are proud to offer you a new and
revised version of our textbook. With this edition, we have listened to you, our users,
and have incorporated many of your suggestions for improvement.
8th
7th
6th
5th
4th
3rd
2nd
1st
In the Eighth Edition, we continue to offer instructors and students a text that is
pedagogicallysound, mathematically precise, and still comprehensible. There are many
changes in the mathematics, art, and design; the more significant changes are noted here.
• New Chapter Openers Each Chapter Openerhas three parts, InMathematics, In
Real Life, and In Careers. In Mathematics describes an important mathematical
topic taught in the chapter. InReal Lifetells students where they will encounter this
topic in real-life situations. In Careers relates application exercises to a variety of
careers.
• New Study Tips and Warning/Cautions Insightful information is given to
students in two new features. The Study Tip provides students with useful
information or suggestions for learning the topic. The Warning/Caution points out
common mathematical errors made by students.
• New Algebra Helps Algebra Help directs students to sections of the textbook
where they can review algebra skills needed to master the current topic.
• New Side-by-Side Examples Throughout the text, we present solutions to many
examples from multiple perspectives—algebraically, graphically, and numerically.
The side-by-side format of this pedagogical feature helps students to see that a problem
can be solved in more than one way and to see that different methods yield the same
result. The side-by-side format also addresses many different learning styles.
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A Word From the Author vii
• New Capstone Exercises Capstonesare conceptual problems that synthesize key
topics and provide students with a better understanding of each section’s
concepts. Capstone exercises are excellent for classroom discussion or test prep, and
teachers may find value in integrating these problems into their reviews of the
section.
• New Chapter Summaries The Chapter Summary now includes an explanation
and/or example of each objective taught in the chapter.
• Revised Exercise Sets The exercise sets have been carefully and extensively
examined to ensure they are rigorous and cover all topics suggested by our users.
Many new skill-building and challenging exercises have been added.
For the past several years, we’ve maintained an independent website—
CalcChat.com—that provides free solutions to all odd-numbered exercises in the text.
Thousands of students using our textbooks have visited the site for practice and help
with their homework. For the Eighth Edition, we were able to use information from
CalcChat.com, including which solutions students accessed most often, to help guide
the revision of the exercises.
I hope you enjoy the Eighth Edition of Trigonometry. As always, I
welcome comments and suggestions for continued improvements.
Acknowledgments
I would like to thank the many people who have helped me prepare the text and the
supplements package. Their encouragement, criticisms, and suggestions have been
invaluable.
Thank you to all of the instructors who took the time to review the changes in this
edition and to provide suggestions for improving it. Without your help, this book would
not be possible.
Reviewers
Chad Pierson, University of Minnesota-Duluth; Sally Shao, Cleveland State University;
Ed Stumpf, Central Carolina Community College; Fuzhen Zhang, Nova Southeastern
University; Dennis Shepherd, University of Colorado, Denver; Rhonda Kilgo,
Jacksonville State University; C. Altay Özgener, Manatee Community College
Bradenton; William Forrest, Baton Rouge Community College; Tracy Cook, University
of Tennessee Knoxville; Charles Hale, California State Poly University Pomona; Samuel
Evers, University of Alabama; Seongchun Kwon, University of Toledo; Dr. Arun K.
Agarwal, Grambling State University; Hyounkyun Oh, Savannah State University;
Michael J. McConnell, Clarion University; Martha Chalhoub, Collin County
Community College; Angela Lee Everett, Chattanooga State Tech Community College;
Heather Van Dyke, Walla Walla Community College; Gregory Buthusiem, Burlington
County Community College; Ward Shaffer, College of Coastal Georgia; Carmen
Thomas, Chatham University
My thanks to David Falvo, The Behrend College, The Pennsylvania State
University, for his contributions to this project. My thanks also to Robert Hostetler, The
Behrend College, The Pennsylvania State University, and Bruce Edwards, University of
Florida, for their significant contributions to previous editions of this text.
I would also like to thank the staff at Larson Texts, Inc. who assisted with proof-
reading the manuscript, preparing and proofreading the art package, and checking and
typesetting the supplements.
On a personal level, I am grateful to my spouse, Deanna Gilbert Larson, for her
love, patience, and support. Also, a special thanks goes to R. Scott O’Neil. If you have
suggestions for improving this text, please feel free to write to me. Over the past two
decades I have received many useful comments from both instructors and students, and
I value these comments very highly.
Ron Larson
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Supplements
Supplements for the Instructor
Annotated Instructor’s Edition This AIE is the complete student text plus point-of-
use annotations for the instructor, including extra projects, classroom activities, teaching
strategies, and additional examples. Answers to even-numbered text exercises,
Vocabulary Checks, and Explorations are also provided.
Complete Solutions Manual This manual contains solutions to all exercises from the
text, including Chapter Review Exercises and Chapter Tests.
Instructor’s Companion Website This free companion website contains an abundance
of instructor resources.
PowerLecture™with ExamView® The CD-ROM provides the instructor with dynamic
media tools for teaching Trigonometry. PowerPoint® lecture slides and art slides of the
figures from the text, together with electronic files for the test bank and a link to the
Solution Builder, are available. The algorithmic ExamView allows you to create, deliver,
and customize tests (both print and online) in minutes with this easy-to-use assessment
system. Enhance how your students interact with you, your lecture, and each other.
Solutions Builder This is an electronic version of the complete solutions manual
available via the PowerLecture and Instructor’s Companion Website. It provides
instructors with an efficient method for creating solution sets to homework or exams
that can then be printed or posted.
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